2017/08/09 by Qingxin Meng, Meng, Qingxin, Qiu‐Hong Shi +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1708.03004
openalex publication_date 2017/08/09 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28
This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain. By Ekeland's variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any ε -near optimal control in a local form with an error order of exact ε % (1)/(2). Moreover, under additional convexity conditions on Hamiltonian function, we prove that an ε -maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.